Events for November 14, 2018 from General and Seminar calendars

Noncommutative Geometry Seminar

Abstract: The Baum-Douglas model for K-homology provides a geometric counterpart to the analytic construction of Kasparov. In the framework of index theory, the former is more related to the topological index, while the latter is more related to the analytic index. I will discuss various relative constructions in geometric (i.e., Baum-Douglas) K-homology and each case the associated index theoretic invariant. If time permits, some more analytic constructions involving Hilsum's notion of KK-bordism will also be discussed. The results in this talk are (in part) joint work with Magnus Goffeng and Bram Mesland.

Groups and Dynamics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Anton Bernshteyn, CMU

Title:Is multiplication of weak equivalence classes continuous?

Abstract: The relations of weak containment and weak equivalence were introduced by Kechris in order to provide a convenient framework for describing global properties of p.m.p. actions of countable groups. Weak equivalence is a rather coarse relation, which makes it relatively well-behaved; in particular, the set of all weak equivalence classes of p.m.p. actions of a given countable group $\Gamma$ carries a natural compact metrizable topology. Nevertheless, a lot of useful information about an action (such as its cost, type, etc.) can be recovered from its weak equivalence class. In addition to the topology, the space of weak equivalence classes is equipped with a multiplication operation, induced by taking products of actions, and it is natural to wonder whether this multiplication operation is continuous. The answer is positive for amenable groups, as was shown by Burton, Kechris, and Tamuz. In this talk, we will explore what happens in the nonamenable case. Number theory will make an appearance.

AMUSE

Abstract: As is well known, univariate interpolation by polynomials is well understood, easy to implement (usually) and has many applications. In the multivariate setting, interpolation by polynomials is far more complicated while the need to interpolate (or almost interpolate) data is very important. In this talk we will discuss how to interpolate data with multivariate polynomials but stress that there are far more effective ways to accomplish this goal. Several applications of multivariate interpolation will be given as well.